Help! - our 3.5yo goes to sleep around midnight

We start bedtime around 8pm. Brush teeth, read a couple books, tell a couple stories. Lights out and I'm out of her room by 8:45pm. She calls me back in a few times while I'm doing dishes / cleaning. Then I walk the dog and go to bed. But I can still hear her footsteps scurrying around her room for another couple hours before she goes to bed.

She is independent from ~9pm on. She turns the light on and does puzzles or flips through picture books. She goes in and out of her bed. She has a Tonies box she listens to.

On weekdays she naps at daycare from 1pm-2:30pm - this doesn't help. She hasn't napped on weekends for awhile but she's now getting to the point where she'll stay up til 11pm on weekends too. I wake her up every morning at 8am - she never wakes on her own so she's clearly tired. She's upset and groggy for a few minutes but then springs to life.

She's high functioning and there are no behavior issues. But I worry she's not getting adequate sleep for her growth & development (she's getting about 9.5 hrs total, from what I've read 11 hrs is average at this age). Also I don't have much time for my wife or myself as the younger one wakes up around 7 and we have another on the way.

Looking for advice. Obviously the nap is not helping but daycare has to offer it and she always chooses to nap and falls asleep on her own. Do I need to stay in her room until she falls asleep? Remove everything from her room but the bed? Ignore this problem as it'll self-resolve when she starts elementary and maybe 9.5 hrs actually is enough sleep?